2. Scenario analysis¶

An essential feature of a model is that when given a specific set of inputs (the exogenous variables to the model) it will always return the same results. As noted when, as was the case of the load, teh moedl is solved without changing any inputs we would expect that the model will return exactly the same data as before. To test this for the mpak we can use compare results from basedf and lastdf dataframes.

Below we are gratified to see that the percent difference between the variables is zero.

# Need statement to change the default format
mpak.smpl(2020,2030)
mpak['PAKNYGDPMKTPKN PAKNECONPRVTKN'].difpctlevel.mul100.df

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [1], in <cell line: 2>()
      1 # Need statement to change the default format
----> 2 mpak.smpl(2020,2030)
      3 mpak['PAKNYGDPMKTPKN PAKNECONPRVTKN'].difpctlevel.mul100.df

NameError: name 'mpak' is not defined

2.1. Different kinds of simulations¶

The modelflow package allows us to do 4 different kinds of simulations:

A shock to an exogenous variable in the model
An exogenous shock of a behavioural variable, executed by exogenizing the variable
An endogenous shock of a behavioural variable, executed by shocking the add factor of the variable.
A mixed shock of a behavioural variable, achieved by temporarily exogenixing the variable.

Although technically modelflow would allow us to shock identities, that would violate their nature as accounting rules so we exclude this possibility.

2.1.1. A shock to an exogenous variable¶

A World Bank model will reproduce the same values if inputs (exogenous variables) are not changed. In the simulation below we change the oil price increasing it by $25 for the three years between 2025 and 2027 inclusive.

To do this we first create a new input dataframe with the revised data.

Then we use the mfcalc method to change the value for the three years in question.

Finally we do a but of pandas math to display the initial value, the changed value and the difference between the two, confirming that the mfcalc statement did what we hoped.

#Make a copy of the baseline dataframe
oilshockdf=mpak.basedf
oilshockdf=oilshockdf.mfcalc("<2025 2027> WLDFCRUDE_PETRO = WLDFCRUDE_PETRO +25")

compdf=mpak.basedf.loc[2000:2030,['WLDFCRUDE_PETRO']]
compdf['LASTDF']=oilshockdf.loc[2000:2030,['WLDFCRUDE_PETRO']]
compdf['Dif']=compdf['LASTDF']-compdf['WLDFCRUDE_PETRO']
compdf

2.1.1.1. Running the simulation¶

Having created a new dataframe comprised of all the old data plus the changed data for the oil price we can execute the simulation. In the command below, the simulation is run from 2020 to 2040, using the oilshockdf as the input dataframe. The results of the simulation will be put into a new dataframe ExogOilSimul. The Keep command ensures that the mpak model object stores (keeps) a copy of the results identified by the text name ‘$25 increase in oil prices 2025-27’.

ExogOilSimul = mpak(oilshockdf,2020,2040,keep='$25 increase in oil prices 2025-27') # simulates the model 

Using the modelflow visualization tools we can see the impacts of the shock; as a print out; as charts and within Jupyter notebook as an interactive widget.

2.1.1.1.1. Results¶

Here we confirm that the shock we wanted to introduce was executed. The dif.df method returns the difference between the selected variable(s) as a dataframe, the smpl method restructs the time period of over which subsequent commands are effectuated.

mpak.smpl(2020,2030)
mpak['WLDFCRUDE_PETRO'].dif.df

Below we look at the impact of this change on a few variables, expressed as a percent deviation of the variable from its pre-shock level.

The first variable PAKNYGDPMKTPKN is Pakistan’s real GDP, the second PAKNECONPRVTKN is real consumption and the third is the Consumer price deflator PAKNECONPRVTXN.

mpak['PAKNYGDPMKTPKN PAKNECONPRVTKN PAKNEIMPGNFSKN PAKNECONPRVTXN'].difpctlevel.mul100.plot(Title="Impact of temporary $25 hike in oil prices")

The graphs show the change in the level as a percent of the previous level. The graphs suggest that a temporary $25 oil price hike would reduce GDP in the first year by about 1.5 percent, that the impact would diminish in the second year to about -.25 percent and that the impact would turn positive in the fourth year when the price effect was eliminated.
The negative impact would on household consumption would be stronger but follow a similar pattern. The reason that the GDP impact is smaller, is partly because of the impact on imports which decline strongly. Because imports enter into the GDP identity with a negative sign they reduce the overall impact on GDP.

Finally as could be expected prices rise sharply initially with higher oil prices, but as the slow down in growth is felt, inflationary pressures turn negative and the overall impact on the price level turns negative. The graph above shows what is happening to the price level. To see the impact on inflation (the rate of growth of prices) we will have to do a separate graph using difpct.mul100, which shows teh change in the rate of growth of variables where the growth rate is expressed as a per cent.

mpak['PAKNECONPRVTXN'].difpct.mul100.plot(Title="Change in inflation from a temporary $25 hike in oil prices")

This view, gives a more nuanced result. Inflation spikes initially by about 1.2 percent, but falls below as the influence of the slowdown weighs on the lagged effect of higher oil prices. In 2028 when oil prices drop back to their previous level this adds to the dis-inflationary forces in the economy at first, but the boost to demand fro lower prices soon translates into an acceleration in growth and higher inflation.

2.2. A shock to a Behavioural variable¶

mpak.PAKGGREVGNFSCN.frml

The result of the equation can be fixes by calling mpak.fix(<dataframe>,PAKGGREVGNFSCN,2023,2023)

This will create a new dataframe where the value of PAKGGREVGNFSCN_X is set to the current value of PAKGGREVGNFSCN, and the value of PAKGGREVGNFSCN_D is set to 1 in the year 2023.
When this dataframe is simulated the value of PAKGGREVGNFSCN will not depend on the ordinary right hand side variables, only on the value of PAKGGREVGNFSCN_X.

alternative_base = mpak.fix(baseline,'PAKGGREVGNFSCN',2023,2023)

Warning

In this experiment PAKGGREVGNFSCN is fixed in 2023. The value in all other years will be calculated using the original equation.
To fix the value for all periods replace 2023,2023 with 2023,2100

2.3. Create a scenario by shocking PAKGGREVGNFSCN¶

A new dataframe where PAKGGREVGNFSCN_X is increased by one percent of GDP is created

alternative = alternative_base.upd(f'<2023 2023> PAKGGREVGNFSCN_X + {baseline.loc[2023,"PAKNYGDPMKTPCN"]*0.01 }')

The variable before and after the shock can be displayed

print(f'Value of GDP in 2023: {baseline.loc[2023,"PAKNYGDPMKTPCN"]:,.0f}')
print(f'Base value in 2023: {alternative_base.loc[2023,"PAKGGREVGNFSCN_X"]:,.0f}. Alternative value: {alternative.loc[2023,"PAKGGREVGNFSCN_X"]:,.0f}.'
    f'Difference: {-(alternative_base.loc[2023,"PAKGGREVGNFSCN_X"]-alternative.loc[2023,"PAKGGREVGNFSCN_X"]):,.0f}.')

2.4. Simulate the model¶

%matplotlib notebook 
result = mpak(alternative,2020,2035,keep='Taxes on Goods and Services up by 1 pct of GDP in 2023') # simulates the model 

2.5. Access results¶

Now we have two dataframes with results baseline and result. These dataframes can be manipulated and visualized with the tools provided by the pandas library and other like Matplotlib and Plotly. However to make things easy the first and latest simulation result is also in the mpak object:

mpak.basedf: Dataframe with the values for baseline
mpak.lastdf: Dataframe with the values for alternative

The result can easily be visualized in Jupyter notebooks by using the [.] operator this will display the values of the variables in square brackets and useful transformations of the values including the impact. In addition the exotenous variables which has changed are displayed.

Click on the tabs to display the different output

mpak['PAKNYGDPMKTPCN PAKNYGDPMKTPKN PAKGGEXPTOTLCN PAKGGREVTOTLCN PAKNECONGOVTKN']

2.6. Or use keep_plot to make more bespoken charts which can be saved in many formats¶

This method can display a number of different transformations of the series for more here
Here only a few:

2.6.1. Differences of growth rates¶

mpak.keep_plot('PAKNYGDPMKTPCN PAKGGEXPTOTLCN',diff=1,showtype='growth',savefig='testgraph/tax_impact_growth_.svg',legend=0);

2.6.2. Differences in percent of baseline values¶

mpak.keep_plot('PAKNYGDPMKTPCN PAKGGEXPTOTLCN',diffpct=1,showtype='level',savefig='testgraph/tax_impact_difpct_.svg',legend=0);

2.7. Some variations on keep_plot(¶

The variables we want to be displayed is listed as first argument. Variable names can include wildcards (using * for any string and ? for any character)

Transformation of data displayed:

showtype=	Use this operator
‘level’ (default)	No transformation
‘growth’	The growth rate in percent
‘change’	The yearly change ($\Delta$)

legend placement

legend=	Use this operator
False (default)	The legends will be placed at the end of the corresponding line
True	The legends are places in a legend box

Often it is useful to compare the scenario results with the baseline result. This is done with the diff argument.

diff=	Use this operator
False (default)	All entries in the keep_solution dictionary is displayed
True	The difference to the first entry is shown.

It can also be useful to compare the scenario results with the baseline result measured in percent. This is done with the diffpct argument.

diffpct=	Use this operator
False (default)	All entries in the keep_solution dictionary is displayed
True	The difference in percent to the first entry is shown

savefig='[path/]<prefix>.<extension>' Will create a number of files with the charts.
The files will be saved location with name <path>/<prefix><variable name>.<extension>
The extension determines the format of the saved file. pdf, svg and png are the most common extensions.

!dir testgraph\

# fixed_alternative = mpak.fix(alternative,'PAKGGEXPCAPTCN PAKGGEXPGNFSCN PAKGGEXPOTHRCN PAKGGEXPTRNSCN',2023,2035)
fixed_alternative = mpak.fix(alternative,'PAKGGEXPCAPTCN ',2023,2035)

result_fixed_expenditure = mpak(fixed_alternative,2020,2035,keep='Taxes on Goods and Services up, expenditure fixed',silent=0,first_test=60) # simulates the model 

mpak.fix_dummy_fixed

mpak['PAKNYGDPMKTPCN PAKNYGDPMKTPKN PAKGGEXPTOTLCN PAKGGREVTOTLCN PAKNECONGOVTKN']

mpak.keep_solutions.keys()

with mpak.keepswitch(scenarios='Taxes on Goods and Services up by 1 pct of GDP in 2023|Taxes on Goods and Services up, expenditure fixed'):
    mpak.keep_plot('PAKNYGDPMKTPCN PAKNYGDPMKTPKN PAKGGEXPTOTLCN PAKGGREVTOTLCN PAKNECONGOVTKN',diff=1,showtype='level',legend=0);

The World Bank's MFMod Framework in Python with Modelflow

Scenario analysis

Contents